congressional laws must always be published.

Another type of executive order is the presidential proclamation. Like the executive memoranda, these also have the force of law, but there is no requirement for them to be published in the federal register. Yet, some presidents do choose to publish their proclamations. For example, President Obama used a proclamation to designate two new national monuments in Utah and Nevada in December of 2016. These monuments were the Bears Ears National Monument in Utah and the Gold Butte National Monument in Nevada. The president invoked the federal Antiquities Act of 1906 as the basis for his proclamation, and the executive order was published in the federal register.

While presidents aren't required to publish proclamations and memoranda, they must publish executive orders. At the same time, there are certain executive orders that are so sensitive in nature that presidents can choose not to make them public. These types of executive orders usually pertain to matters of national security, and they are called presidential policy directives (PPD). President Obama purportedly made 30 PPDs during his time as president; however, only 11 of those were released. As part of a body of secret law, PPDs are not required to be released to the general public.

All presidents have used PPDs in some form or other. President Clinton called his national security directives PDDs or Presidential Decision Directives. On the other hand, President Bush called his directives National Security Presidential Directives (NSPD).

So, a major difference between executive orders and congressional laws is that certain types of executive orders aren't required to be made public or to be recorded in the federal register. In contrast, all congressional laws must be recorded and published.

In terms of their powers, there is no difference between an executive order and a law.  Executive orders have the force of law and must be obeyed unless they are overturned by some competent authority, like the Supreme Court.

The major difference between the two comes in how they are made.  A law must go through the entire legislative process.  It must be approved by both houses of Congress and signed by the President.  By contrast, an executive order does not have to do any of these things.  A president can simply draft and issue an executive order without any formal approval from any other part of government. 

Thus, both executive orders and laws have the force of law and must be obeyed, but the two are created in very different ways.

An executive order is a privilege of the executive branch of government, i.e. the President of the United States. The President is permitted to sign an executive order that he or she believes to be lawful based on the US Constitution. The President can bypass Congress with an executive order; however, once signed into law, the order can be challenged in court. For example, in June of 2016, the Supreme Court heard challenges to President Obama's DREAM Act, an executive order he issued regarding immigration. Rather than ruling, the Supreme Court sent the individual challenges (representing 26 states) back to their respective lower courts, where those courts could toss out or uphold the order. 

A law must pass through the legislative branch of government, i.e. Congress. Both the House of Representatives and Senate have a role in making a bill a law. Once a bill has passed through both branches of Congress, the President will sign the bill into law or veto it. Congress can override the President's veto with a two-thirds majority.